Deep Learning based discovery of Integrable Systems

• URL: http://arxiv.org/abs/2503.10469v2
• Date: Sun, 16 Mar 2025 15:48:53 GMT
• Title: Deep Learning based discovery of Integrable Systems
• Authors: Shailesh Lal, Suvajit Majumder, Evgeny Sobko,
• Abstract summary: We introduce a novel machine learning based framework for discovering integrable models.<n>Our approach first employs a synchronized ensemble of neural networks to find high-precision numerical solution to the Yang-Baxter equation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a novel machine learning based framework for discovering integrable models. Our approach first employs a synchronized ensemble of neural networks to find high-precision numerical solution to the Yang-Baxter equation within a specified class. Then, using an auxiliary system of algebraic equations, [Q_2, Q_3] = 0, and the numerical value of the Hamiltonian obtained via deep learning as a seed, we reconstruct the entire Hamiltonian family, forming an algebraic variety. We illustrate our presentation with three- and four-dimensional spin chains of difference form with local interactions. Remarkably, all discovered Hamiltonian families form rational varieties.

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